Higher-order topological phases host robust boundary states at the boundary of the boundary, which can be interpreted from their boundary topology. In this work, we show that based on the surface states of a weak topological insulator, the interplay between superconductors and magnetic fields can lead to the various helical or chiral Majorana hinge modes and even corner modes. Particularly, the obtained higher-order topological superconductors (TSCs) can be attributed to their certain boundaries, surfaces, or hinges, which naturally behave as a TSC in DIII or D symmetry class. Correspondingly, these higher-order TSCs can be characterized by the boundary topological invariants, such as surface Chern numbers or surface $Z_2$ topological invariants for surface TSCs. Remarkably, some chiral hinge states naturally form the Majorana interference loop without complicated heterostructure, revealing the exceptional property of higher-order TSCs. Our models not only can be realized in iron-based superconductors with desired inverted band structures and superconducting pairings, but also pave the way to the implementation of quantum interference device from the higher-order topological matters.

中文翻译：

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基于弱拓扑绝缘体的高阶拓扑超导体

高阶拓扑相在边界的边界处具有稳健的边界状态，这可以从它们的边界拓扑中得到解释。在这项工作中，我们表明基于弱拓扑绝缘体的表面状态，超导体和磁场之间的相互作用可以导致各种螺旋或手性马约拉纳铰链模式甚至角模式。特别是，获得的高阶拓扑超导体（TSC）可以归因于它们的某些边界、表面或铰链，它们自然地表现为 DIII 或 D 对称类中的 TSC。相应地，这些高阶 TSC 可以通过边界拓扑不变量来表征，例如表面陈数或表面$Z_2$表面 TSC 的拓扑不变量。值得注意的是，一些手性铰链态自然形成了马约拉纳干涉环，没有复杂的异质结构，揭示了高阶 TSC 的特殊性质。我们的模型不仅可以在具有所需倒带结构和超导配对的铁基超导体中实现，而且还为从高阶拓扑问题实现量子干涉装置铺平了道路。